Madame Olympe Maxime is the Love Interest of Rubeus Hagrid in the Harry Potter novels and movies. She is played by Frances de la Tour in the films.
Madame Maxime was, like Hagrid, one of the last surviving civilized Giants, but unlike him, she was embarrassed of this and she tried to say she had "big bones" which was a stupid move amongst wizards who would know of her true identity. Madame Maxime had been Headmistress of Beauxbatons Academy for some time and took part in politics, in France and Britain's Ministry of Magic. She was obviously part of the International Confederation of Wizards, like her colleague, Karkaroff of Durmstrang Academy.
Like Karkaroff, she had a favourite student - Fleur was her favourite and she got selected for Triwizard Champion.
Madame Maxime first appears when her carriage arrives at Hogwarts School. She is accompanied by her students, and is very elegant despite her alarming size. Even Harry, who is used to Hagrid, is surprised by her enormity. Madame Maxime is introduced to Hagrid by Professor Dumbledore, who says Hagrid will look after her winged horses. Madame Maxime likes Dumbledore, and she has met him before.
Madame Maxime is seen moving around the castle with her students after the Welcoming Feast. She takes them back to their carriage, which is like a trailer home for them. Madame Maxime is later seen having her students submit their names in the Goblet of Fire, for entering the Tournament. Madame Maxime first makes her romantic advancements to Hagrid when he puts on his best suit, and gels his hair, and abandons Harry, Ron and Hermione to walk up to the castle with Madame Maxime, who is looking very elegant and smart. Ron jokes that if they end up married, they'll have a record for the size of a baby.
Later, when the Champions are announced at Halloween, Madame Maxime is delighted Fleur entered, but she is very angered when someone submits Harry for a fourth Champion. Madame Maxime yells at Dumbledore, saying its his fault, and that she'll be complaining to the government. Karkaroff also agrees it's been fixed. However, Bagman, the Tournament manager, says its not fixed and it must continue as it is, regardless of this fluke. Madame Maxime seems to vent herself down after berating Dumbledore with Fleur (in French, of course).
When the First and Second Tasks are over, the Yule Ball is unexpectedly announced, which is a Christmas get-together ball. Inevitably, Hagrid asks Madame Maxime to accompany him. She does, and their romance blossoms. But it breaks up when Hagrid asks Madame Maxime if she's a Giantess, and she angrily shouts she just has big bones. As Harry says, "I dunno who she thinks she's kidding. If Hagrid's half-Giant, she definitely is."
Then, Madame Maxime breaks up with Hagrid for the remainder of the year, making him gloomy and suicidal. He sinks even lower when journalist Rita Skeeter hits a scoop on them both being half Giant, making Hagrid think everyone hates him because of this. But Dumbledore insists Hagrid come back to work. Later, Voldemort returns in the Third Task, and kills Cedric, the Champion, but almost kills Harry. Madame Maxime is distraught at the news.
Later, Madame Maxime put their grudge behind them and bond again to go and recruit the Giants for Dumbledore since Fudge, the Minister, doesn't believe Voldemort is really back. Madame Maxime impresses Hagrid by roughing it out, since he believed she'd complain, because she looks too elegant to go rough. But she goes journeying with him with no complaint. They get to the Giants, and are almost on the point of recruiting the Giant Gurg Karkus, when suddenly Death Eaters arrive and organize a rebellion, and have Golgomath kill Karkus and take his place. The Giants are driven away by Death Eaters, leaving only Golgomath and his evil Giants alive. However, the mission is not all a failure - Hagrid finds his half-brother Grawp, and drags him back because Grawp was being bullied by the other Giants. Madame Maxime gets weary of Grawp but she doesn't complain. Eventually she parts with Hagrid, and returns to Beauxbatons, agreeing not to tell anyone of Grawp.
When Dumbledore is killed by Snape, Madame Maxime takes the carriage to Hogwarts, and falls sobbing into Hagrid's arms, and they are together at Dumbledore's funeral.
Its unknown if they continued their relationship after the war ended.